On module extension Banach algebras

Document Type : Research Paper



Let $A$ be a Banach algebra and $X$ be a Banach $A$-bimodule. Then
${mathcal{S}}=A oplus X$, the $l^1$-direct sum of $A$ and $X$
becomes a module extension Banach algebra when equipped with the
algebra product $(a,x).(a',x')=(aa',ax'+xa').$ In this paper, we
investigate biflatness and biprojectivity for these Banach algebras.
We also discuss on automatic continuity of derivations on ${mathcal{S}}=Aoplus A$.